Let $f(x) = -4x^{2}+3x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Answer: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-4x^{2}+3x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -4, b = 3, c = 1$ $ x = \dfrac{-3 \pm \sqrt{3^{2} - 4 \cdot -4 \cdot 1}}{2 \cdot -4}$ $ x = \dfrac{-3 \pm \sqrt{25}}{-8}$ $ x = \dfrac{-3 \pm 5}{-8}$ $x =-\frac{1}{4},1$